A Phenomenological analysis on isospin-violating decay of $X(3872)$

Abstract

In a molecular scenario, we investigate the isospin-breaking hidden charm decay processes of $X(3872)$, i.e., $X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$, $X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^{0}J/\psi$, and $X(3872)\to {\pi }^0{\chi }_{cJ}$. We assume that the source of the strong isospin violation comes from the different coupling strengths of $X(3872)$ to its charged components $D^{\ast +}{D}^{-}$ and neutral components $D^{\ast 0}{\bar{D}}^0$ as well as the interference between the charged meson loops and neutral meson loops. The former effect could fix our parameters by using the measurement of the ratio $\Gamma [X(3872)\to {\pi }^{+}{\pi }^{-}{\pi }^{0}J/\psi ]/\Gamma [X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi ]$. With the determined parameter range, we find that the estimated ratio $\Gamma [X(3872)\to {\pi }^0{\chi }_{c1}/\Gamma [X(3872)\to {\pi }^{+}{\pi }^{-}J/\psi ]$ is well consistent with the experimental measurement from the BESIII collaboration. Moreover, the partial width ratio of ${\pi }^0{\chi }_{cJ}$ for $J=0,1,2$ is estimated to be $1.77\sim 1.65:1:1.09\sim 1.43$, which could be tested by further precise measurements of BESIII and Belle II.

arXiv comment11 pages, 7 figures, accepted for publication in the Eur.Phys.J.C

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• The double thresholds distort the lineshapes of the $P_{\psi s}^{\Lambda }(4338{)}^0$ resonance
• Revisit the isospin violating decays of $X(3872)$
• Productions of $X(3872)$, $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in $B_{(s)}$ decays offer strong clues on their molecular nature
• Observation of sizeable $\omega$ contribution to ${\chi }_{c1}(3872)\to {\pi }^{+}{\pi }^{-}J/\psi$ decays
• The possibility of $X(4014)$ as a $D^{\ast }{\bar{D}}^{\ast }$ molecular state
• Production of $Z_{cs}$ in $B$ and $B_s$ decay
• Hidden-bottom hadronic transitions of ${\rm Y}(10753)$
• hidden charm decays of $X(4014)$ in a $D^{\ast }{\bar{D}}^{\ast }$ molecule scenario
• Dispersive analysis of the isospin breaking in the $X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$ and $X(3872)\to J/\psi {\pi }^{+}{\pi }^0{\pi }^{-}$ decays
• Study of exotic hadrons with machine learning
• ${\bar{B}}^0\to {\bar{K}}^{(\ast )0}X$, $B^{-}\to K^{(\ast )-}X$, ${\bar{B}}_s^0\to \eta ({\eta }^{\prime },\varphi )X$ from the $X(3872)$ molecular perspective
• Search for $X(3872)\to {\pi }^0{\chi }_{c0}$ and $X(3872)\to \pi \pi {\chi }_{c0}$ at BESIII
• Pole trajectories from $S$- and $P$-wave $D{\bar{D}}^{\ast }$ interactions
• Constrain the ${\chi }_{cJ}\to D^{(\ast )}{\bar{D}}^{(\ast )}$ effective couplings via the $X(3872)\to {\pi }^0{\chi }_{cJ}$ decays
• The $X(3872)\to J/\psi \pi \gamma$ and $X(3872)\to J/\psi \pi \pi \gamma$ decays
• Two-body strong decays of the hidden-charm tetraquark molecular states via the QCD sum rules
• Exotic hadrons associated with $b$-quark
• Insights into the nature of the $X(3872)$ through B meson decays